Problem: Simplify the following expression and state the condition under which the simplification is valid. $t = \dfrac{x^2 - 4}{x + 2}$
First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = x$ $ b = \sqrt{4} = 2$ So we can rewrite the expression as: $t = \dfrac{({x} + {2})({x} {-2})} {x + 2} $ We can divide the numerator and denominator by $(x + 2)$ on condition that $x \neq -2$ Therefore $t = x - 2; x \neq -2$